Let A be the set of all `3xx3` skew-symmetric matrices whose entries are either -1, 0, or 1. If there are exactly three 0's, three 1's, and three (-1)'s, then the number of such matrices is __________ .

Let A be the set of all 3xx3 skew-symmetri matrices whose entries are either -1,0,or1. If there are exactly three 0s three 1s, and there (-1)' s , then the number of such matrices is __________.

Let A be the set of all 3 xx 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A is

Let A be the set of all 3xx3 symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices A in A for which the system of linear equations A[(x),(y),(z)]=[(1),(0),(0)] is inconsistent is

Let A be the set of all 3xx3 symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices A in A for which the system of linear equations A[(x),(y),(z)]=[(1),(0),(0)] has a unique solution is

If A is a 3xx3 skew-symmetric matrix, then trace of A is equal to -1 b. 1 c. |A| d. none of these

Let A=[a_("ij")] be a matrix of order 2 where a_("ij") in {-1, 0, 1} and adj. A=-A . If det. (A)=-1 , then the number of such matrices is ______ .

Find the number of all possible matrices of order 3xx3 with each entry 0 or 1. How many of these are symmetric ?

Let omega!=1 be cube root of unity and S be the set of all non-singular matrices of the form [(1,a, b), (omega, 1, c), (omega^2, omega, 1)] , where each of a ,b and c is either omegaoromega^2 Then the number of distinct matrices in the set S is a. 2 b. 6 c. 4 d. 8

If the entries in a 3xx3 determinant are either 0 or 1, then the greatest value of their determinants is

The number of 3xx3 matrices A whose entries are either 0or1 and for which the system A[x y z]=[1 0 0] has exactly two distinct solution is a. 0 b. 2^9-1 c. 168 d. 2